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Researchers frequently wish to assess the equality or inequality of groups, but this comes with the challenge of adequately adjusting for multiple comparisons. Statistically, all possible configurations of equality and inequality constraints can be uniquely represented as partitions of the groups, where any number of groups are equal if they are in the same partition. In a Bayesian framework, one can adjust for multiple comparisons by constructing a suitable prior distribution over all possible partitions. Inspired by work on variable selection in regression, we propose a class of flexible beta-binomial priors for Bayesian multiple comparison adjustment. We compare this prior setup to the Dirichlet process prior suggested by Gopalan and Berry (1998) and multiple comparison adjustment methods that do not specify a prior over partitions directly. Our approach to multiple comparison adjustment not only allows researchers to assess all pairwise (in)equalities, but in fact all possible (in)equalities among all groups. As a consequence, the space of possible partitions grows quickly - for ten groups, there are already 115,975 possible partitions - and we set up a stochastic search algorithm to efficiently explore the space. Our method is implemented in the Julia package EqualitySampler, and we illustrate it on examples related to the comparison of means, variances, and proportions., Comment: 25 pages, 9 figures, and 1 table

Testing the equality of two proportions is a common procedure in science, especially in medicine and public health. In these domains it is crucial to be able to quantify evidence for the absence of a treatment effect. Bayesian hypothesis testing by means of the Bayes factor provides one avenue to do so, requiring the specification of prior distributions for parameters. The most popular analysis approach views the comparison of proportions from a contingency table perspective, assigning prior distributions directly to the two proportions. Another, less popular approach views the problem from a logistic regression perspective, assigning prior distributions to logit-transformed parameters. Reanalyzing 39 null results from the New England Journal of Medicine with both approaches, we find that they can lead to markedly different conclusions, especially when the observed proportions are at the extremes (i.e., very low or very high). We explain these stark differences and provide recommendations for researchers interested in testing the equality of two proportions and users of Bayes factors more generally. The test that assigns prior distributions to logit-transformed parameters creates prior dependence between the two proportions and yields weaker evidence when the observations are at the extremes. When comparing two proportions, we argue that this test should become the new default., Comment: 16 pages, 7 figures

Human social behavior plays a crucial role in how pathogens like SARS-CoV-2 or fake news spread in a population. Social interactions determine the contact network among individuals, while spreading, requiring individual-to-individual transmission, takes place on top of the network. Studying the topological aspects of a contact network, therefore, not only has the potential of leading to valuable insights into how the behavior of individuals impacts spreading phenomena, but it may also open up possibilities for devising effective behavioral interventions. Because of the temporal nature of interactions - since the topology of the network, containing who is in contact with whom, when, for how long, and in which precise sequence, varies (rapidly) in time - analyzing them requires developing network methods and metrics that respect temporal variability, in contrast to those developed for static (i.e., time-invariant) networks. Here, by means of event mapping, we propose a method to quantify how quickly agents mingle by transforming temporal network data of agent contacts. We define a novel measure called 'contact sequence centrality', which quantifies the impact of an individual on the contact sequences, reflecting the individual's behavioral potential for spreading. Comparing contact sequence centrality across agents allows for ranking the impact of agents and identifying potential 'behavioral super-spreaders'. The method is applied to social interaction data collected at an art fair in Amsterdam. We relate the measure to the existing network metrics, both temporal and static, and find that (mostly at longer time scales) traditional metrics lose their resemblance to contact sequence centrality. Our work highlights the importance of accounting for the sequential nature of contacts when analyzing social interactions., Comment: 14 pages, 4 fugures, separate supplementary information in pdf

Testing the (in)equality of variances is an important problem in many statistical applications. We develop default Bayes factor tests to assess the (in)equality of two or more population variances, as well as a test for whether the population variances equal a specific value. The resulting test can be used to check assumptions for commonly used procedures such as the $t$-test or ANOVA, or test substantive hypotheses concerning variances directly. We show that our Bayes factor fulfills a number of desiderata. Researchers may have directed hypotheses such as $\sigma_{1}^{2} > \sigma_{2}^{2}$, they may want to extend $\mathcal{H}_{0}$ to have a null-region, or wish to combine hypotheses about equality with hypotheses about inequality, for example $\sigma_{1}^{2} = \sigma_{2}^{2} > (\sigma_{3}^{2}, \sigma_{4}^{2})$. We extend our Bayes factor test to allow for these deviations from our proposed default and illustrate it on a number of practical examples. Our procedure is implemented in the R package $bfvartest$.